Topological Link Models of Multipartite Entanglement

Ning Bao1, Newton Cheng2, Sergio Hernández-Cuenca3, and Vincent Paul Su2

1Computational Science Initiative, Brookhaven National Lab, Upton, NY, 11973, USA
2Center for Theoretical Physics, Department of Physics, University of California, Berkeley, CA 94720, USA
3Department of Physics, University of California, Santa Barbara, CA 93106, USA

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Abstract

We introduce a novel model of multipartite entanglement based on topological links, generalizing the graph/hypergraph entropy cone program. We demonstrate that there exist link representations of entropy vectors which provably cannot be represented by graphs or hypergraphs. Furthermore, we show that the contraction map proof method generalizes to the topological setting, though now requiring oracular solutions to well-known but difficult problems in knot theory.

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► References

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Cited by

[1] Sergio Hernández-Cuenca, Veronika E. Hubeny, and Massimiliano Rota, "The holographic entropy cone from marginal independence", arXiv:2204.00075.

[2] Matteo Fadel and Sergio Hernández-Cuenca, "Symmetrized holographic entropy cone", Physical Review D 105 8, 086008 (2022).

[3] Howard J. Schnitzer, "The entropy cones of $W_N$ and $W_N^d$ states", arXiv:2204.04532.

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